Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C25×C4 |
| direct product | C41×#2679 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C41 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
1000 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7734, C41×#7750, C41×#7786, … |
| maximal normal subgroup of | C41×#7734, C41×#7750, C41×#7786, … |
| maximal quotient of | C41×#14357, C41×#14440, C41×#14535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1411);